The problem is to prove that when . I tried substituting and but then I got stuck. I tried many other things but this was the only notable one.
thanks.
Just in case a picture helps...
... where (key in spoiler) ...
Spoiler:
Larger
Solve the bottom row (for dy/dx).
Edit: ... which is easier said than done. Wolfram doesn't have any better ideas: differentiate x sqrt(y+1) + y sqrt(x+1) = 0 with respect to x - Wolfram|Alpha.
Ok, I'm beginning to see the tan^2 idea...
... nah! Was it suggested? What is the context?
I took the original equation, moved one term to the RHS, squared both sides of the resulting equation and arrived at this quadratic equation ...
using the quadratic formula ...
which simplifies to either (which, by inspection, does not work in the original equation) or
the derivative of the second equation is
might be some other way, but I don't see it ...